Solve for $x$, $ \dfrac{x - 4}{10x} = \dfrac{4}{5x} - \dfrac{3}{20x} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $10x$ $5x$ and $20x$ The common denominator is $20x$ To get $20x$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{x - 4}{10x} \times \dfrac{2}{2} = \dfrac{2x - 8}{20x} $ To get $20x$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{4}{5x} \times \dfrac{4}{4} = \dfrac{16}{20x} $ The denominator of the third term is already $20x$ , so we don't need to change it. This give us: $ \dfrac{2x - 8}{20x} = \dfrac{16}{20x} - \dfrac{3}{20x} $ If we multiply both sides of the equation by $20x$ , we get: $ 2x - 8 = 16 - 3$ $ 2x - 8 = 13$ $ 2x = 21 $ $ x = \dfrac{21}{2}$